Great Stellated Dodecahedron

Great Stellated Dodecahedron is one of semi-regular solids. First discovered in 1568 by Wenzel Jamnitzer, it was rediscovered by Kepler (and published in his Harmonice Mundi in 1619), and the again by Louis Poinsot (1777-1859) in 1809. It belongs to the class of Kepler-Poinsot solids

The great stellated dodecahedron is beilt on top of a regular icosahedron by attaching a triangular pyramid to very face of the latter. It follows that a great stellated dodecahedron has 32 verices, 90 edges, and 60 faces. Euler's theorem is again quite easy to verify.